On semigroups of order-preserving transformations with the same fix set

AYIK G., AYIK H., Koppitz J.

Czechoslovak Mathematical Journal, 2026 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2026
  • Doi Numarası: 10.21136/cmj.2026.0504-24
  • Dergi Adı: Czechoslovak Mathematical Journal
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Anahtar Kelimeler: (completely) isolated subsemigroup, 20M05, 20M20, generating set, order-preserving transformation, orientation-preserving, rank
  • Çukurova Üniversitesi Adresli: Evet

Özet

Let On be the semigroup of all order-preserving (full) transformations on the finite chain Xn = {1,…,n} under its natural order. For a singular idempotent ξ, it is shown that On(ξ)={α∈On:αm=ξfor somem∈N} is a maximal nilpotent subsemigroup of On with zero ξ. Moreover, for a nonempty subset Y of Xn, we give a necessary and sufficient condition for the set On(Y) to be a subsemigroup. Then we find a unique minimal generating set, and so rank, of On(Y) whenever it is a subsemigroup of On. Every subset Y of Xn such that On(Y) is (completely) isolated was characterized.